I want to replace my Broadband router (Speedport W 701V with integrated DSL modem) with a Ubuntu server equipped with a dual port network interface. Can I connect the server directly to the DSL filter? I guess the answer is no and I need a DSL modem to replace the router with my Ubuntu server, but I just want to be sure ...

ADSL is full duplex; Ethernet is typically full duplex but uses multiple half-duplex lines.

ADSL uses G.DMT or G.992 modulation (which is sophisticated enough to require "training" by each end before data can be transmitted and received); Ethernet uses a relatively simpler pulse amplitude modulation (although with 5 levels). Modulation is the method of transmitting/receiving the digital information (i.e. the bits) over an analog medium, e.g. electrically on copper wire(s).

ADSL will encapsulate the payload (the Ethernet frames) within its own protocols (e.g. ATM), so the framing at the protocol layer is incompatible even if you could solve the electrical issues.

If you want to connect to the phone line with an ADSL filter, you should connect to the phone modem port, which is often still built into laptops.

BTW when you connect to a filtered ADSL line, you get the low frequency, low bandwidth (4KHz) voice band. The ADSL data band is above 20KHz, which would be attenuated by the filter.